In applications requiring the summing of a large number of output from klystrons launching TE01 mode waves into cylindrical waveguides, it has been necessary to first convert the waves to TE00 functional waves, and summing according to prior art techniques.
Examples of prior art power combiners are the class of circular power combiners such as U.S. Pat. No. 5,446,426 by Wu et al, which describes a device accepting microwave power from the resonant cavity of a microwave oscillator, and summing into a circularly symmetric waveguide for delivery to an output port. U.S. Pat. No. 4,175,257 by Smith et al describes another circular power combiner comprising radial input ports which furnish microwave power which is summed along a principal axis. U.S. Pat. No. 4,684,874 by Oltman describes another radially symmetric power combiner/divider, and U.S. Pat. No. 3,873,935 describes an elliptical combiner, whereby input energy is provided to one focus of the ellipse, and removed at the other focus. In all of these combiners, the output port is orthogonal to the input port, and the wave mode is TM, rather than TE.
U.S. Pat. No. 4,677,393 by Sharma describes a power combiner/splitter for TE waves comprising an input port, a parabolic reflector, and a plurality of output ports.
For complete understanding of the present invention, a review of well-known traveling wave principles relevant to the prior art should be explained. References for traveling wave phenomenon are “Fields and Waves in Communication Electronics” by Ramo, Whinnery, and Van Duzer, Chapter 7 “Gyrotron output launchers and output tapers” by Mobius and Thumm in “Gyrotron Oscillators” by C. J. Edgcombe, and “Open Waveguides and Resonators” by L. A. Weinstein.
Circular waveguides support a variety of traveling wave types. Modes are formed by waves which propagate in a given phase with respect to each other. For a given free-space wavelength λ, a circular waveguide is said to be overmoded if the diameter of the waveguide is large compared to the wavelength of a wave traveling in it. An overmoded waveguide will support many simultaneous wave modes traveling concurrently. If the wave propagates axially down the waveguide, the wave is said to be a symmetric mode wave. If the wave travels helically down the waveguide, as shown in FIG. 16, the wave is said to be an asymmetric mode wave. In the case where two identical asymmetrical helical waves are combined, the result is an asymmetric wave mode propagating axially. In the case of the present invention, helically propagating waves will be considered.
Transverse electric, transverse magnetic, or hybrid modes propagating in cylindrical waveguides have two integer indices. The first index is the azimuthal index m which corresponds to the number of variations in the azimuthal direction, and the second index is the radial index n that corresponds to the number of radial variations of the distribution of either the electric or magnetic field component. While the radial index n always has to be larger than zero, the azimuthal index m can be equal to zero. Due to their azimuthal symmetry, modes with m=0 are called symmetric modes whereas all other modes are called asymmetric. Asymmetric modes can be composed of a co- and counter-rotating mode with has the consequence that—as in the case of symmetric modes—the net power flow (real part of the poyntingvector) only occurs in the axial direction. However, if either to co- or counter-rotating mode is present there is a net energy flow in axial and azimuthal direction, hence we obtain a helical propagation. For the present invention helically propagating or symmetric modes are considered.
When using a ray-optical approach to the modes, a decomposition of the modes as plane waves with the limit of zero wavelength rays are obtained. In general, these are tangent to a caustic with a radius:Rc=Rw(m/Xmn) where:                Rc is the radius of the caustic        Rw is the radius of the waveguide        Xm is the eigenvalue of the mode        
This has the consequence that the geometrical rays have an azimuthal, radial, and axial coordinate. However, in the case of symmetric modes, the radius of the caustic becomes zero, and hence the rays representing symmetric modes only have a radial and an axial component. In the design of a reflector, the phase front of the rays tangent to a caustic is required. In an asymmetric mode, this phase front is the involute of the caustic. For a symmetric mode, the phase front reduces to a point representing the caustic with a radius=0.
In a cylindrical waveguides, the radial component of the ray does not contribute to the net flow. This however changes as soon as the waveguides has a port which causes a net power flow in the radial direction.
The phase front for an asymmetric mode wave is described by an involute in free space, a shape which is inwardly curled towards the center of the waveguide. The particular shape for the phase front for each wave mode unique, and is generally numerically calculated. The important aspect of the phase front is that it defines a particular surface, and this phase front will be used later for construction of certain structures of the invention.
Traveling waves can also be described in terms of the propagation velocity in a particular direction. Symmetric waves traveling down the axis of the waveguide have a purely axial component, and no perpendicular component. Asymmetric waves traveling helically down the axis of a waveguide have both an axial component, and a perpendicular component. There is a wave number k=2π/λ, where λ is the wavelength of the traveling wave. In each axial (parallel) direction and transverse (perpendicular) direction of travel, the following wave numbers may be computed:kperp=Xmn/Rw kpar=sqrt{k2=kperp2}In these calculations,                Xmn is the eigenvalue of the mode        m is the azimuthal index        Rw is the waveguide radius.        
For asymmetric mode waves, the internally reflecting waves define a circle within the waveguide radius Rw known as a caustic. The radius of the caustic for an asymmetric mode wave isRc=Rw(m/Xmn) Where                Rc=radius of caustic        Rw=radius of waveguide        m=azimuthal index        n=radial index        Xmn is the eigenvalue of the mode        
In cylindrical waveguides, the distance Lc represents the length of waveguide for which propagating TEmn, TMmn, or HEmn waves propagating in a cylindrical wavelength complete a 2n phase change. The formula for Lc isLc=2πRw{kparsqrt{1=(m/Xmn)2}}/{kperpcos−1(m/Xmn)}where                Rw, m, n, Xmn, kperp, kpar are as previously defined        